On Friday, an unnamed Israeli official tried to downplay the significance of the visit, telling the Haaretz daily, "We have nothing to hide."
The official added that Israel would point out to the ICC that it "has neither the authority nor the justification to handle the Palestinians' complaints."
Nahshon told Al Jazeera: "The goal is to give the ICC a better grasp on Israel's legal and judicial system." However, he continued, "That will make things easier if we move to another stage," -- an apparent reference to the possibility that the ICC may consider launching a formal investigation.
Ghazi Hamad, a Palestinian official dealing with ICC matters, said the Palestinian Authority hoped that the visit would "speed up the opening of the investigation" by the court into Israel's conduct during Protective Edge.
"That would provide a clear message to Israel that it cannot continue to commit crimes with impunity," he told Al Jazeera. Hamad said the PA was not told whether the ICC had requested or was granted permission from Israel to access Gaza.
This is the first time Israel has agreed to cooperate with an international body over allegations that could ultimately lead to war crimes trials. Israel denied entry to UN commissions of inquiry in 2009 and 2014, following major offensives in Gaza.
Officials in Washington have repeatedly voiced their opposition to the ICC exercising jurisdiction over Israeli nationals. Neither the US nor Israel has ratified the Rome Statute, the document establishing The Hague court in 2002.
Sari Bashi, director of the Israel-Palestine branch of HRW, said Israel's continuing restrictions on human rights organizations entering Gaza had further undermined the credibility of Israel's investigations. The strict controls had made it "more difficult for [the groups] to do their jobs and to bring relevant information to light," she told Al Jazeera.
Israeli authorities, she added, had previously conceded that human rights groups played an important role in helping to "overcome the fear that Palestinian residents have of meeting [Israeli military] personnel."
Al Mezan and Adalah said that, in many cases, Israel had refused to speak to any witnesses outside the military before it dropped inquiries into suspected war crimes.
Israel has received a total of 500 complaints relating to 360 incidents in Gaza in which there are suspicions of violations of international law.
So far, only a handful of investigations have been opened, relating mainly to physical assaults on civilians, "unlawful firing" at buildings, and looting. On August 24, Israeli announced the closure of more than 93 cases. In 80 cases, no formal investigation was conducted.
Two years on, Israel is still undecided whether to scrutinize some of the most contentious phases of its offensive, including the massive bombardment of Rafah to prevent an Israeli soldier from being taken as prisoner. The incident, known as Black Friday, is believed to have killed more than 100 Palestinian residents of the area.
Aida Burnett-Cargill, a spokeswoman in Gaza for Al Mezan, said Palestinian human rights organizations had sent to the ICC Palestinian witness statements relating to Black Friday in March.
"We hope these materials and others are raising doubts in the minds of the ICC's prosecutors about the seriousness with which Israel is handling its investigations," she told Al Jazeera.
Hamad said that the Palestinian foreign minister, Riad al-Malki, had met the ICC prosecutor, Fatou Bensouda, in The Hague on Friday to promise any help the court might need to launch a formal investigation.
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